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Ask the Wizard #151
Arian from Luton
Yes, my basic strategy charts are designed to be the best play based on the first two cards. This is the usual approach to developing the basic strategy. One benefit to this approach is the expected values of each play can be calculated exactly and compared to other sources. However, you bring up a valid point. So I asked Don Schlesinger, author of Blackjack Attack, if there were any known play where the best play on the initial hand is different from the best play to maximize the expected value of the overall game of blackjack. He replied that a soft 18 against a dealer ace, in a double-deck game, where the dealer stands on soft 17, was such a play. As my blackjack appendix 9 shows the expected value for standing is -0.100502 and for hitting is -0.100359. So, based on the first two cards, the odds favor hitting by 0.000143. However, there are many more ways to see soft 18 than one ace and one seven. The following table shows all the ways this hand can turn up.
Soft 18 Vs Ace Combinatorial Analysis
| Player cards |
Conditional Probability |
Hit EV |
Stand EV |
Hit Return |
Stand Return |
| A7 | 0.621139169 | -0.100359 | -0.100502 | -0.062336906 | -0.062425729 |
| A6A | 0.036728229 | -0.11202 | -0.116009 | -0.004114296 | -0.004260805 |
| A52 | 0.146912917 | -0.111299 | -0.103382 | -0.016351261 | -0.015188151 |
| A43 | 0.146912917 | -0.114804 | -0.103721 | -0.01686619 | -0.015237955 |
| A5AA | 0.001827682 | -0.111395 | -0.105122 | -0.000203595 | -0.00019213 |
| A42A | 0.016814677 | -0.116975 | -0.108233 | -0.001966897 | -0.001819903 |
| A33A | 0.007356421 | -0.132142 | -0.107256 | -0.000972092 | -0.00078902 |
| A322 | 0.020470041 | -0.134229 | -0.11004 | -0.002747673 | -0.002252523 |
| A4AAA | 0.000073486 | -0.117554 | -0.110984 | -0.000008639 | -0.000008156 |
| A32AA | 0.001028802 | -0.134775 | -0.112433 | -0.000138657 | -0.000115671 |
| A222A | 0.000709873 | -0.136788 | -0.114993 | -0.000097102 | -0.00008163 |
| A3AAAA | 0.000002238 | -0.135313 | -0.114821 | -0.000000303 | -0.000000257 |
| A22AAA | 0.000023502 | -0.137312 | -0.117376 | -0.000003227 | -0.000002759 |
| A2AAAAA | 0.000000046 | -0.137859 | -0.119823 | -0.000000006 | -0.000000006 |
| Total | 1 | -0.105806844 | -0.102374694 |
Explanation of column titles
Player cards:Cards in player’s hand
Conditional probability: Given that the player has a soft 18 against a dealer ace the probability of the given hand composition.
Hit EV:Expected value by hitting
Stand EV:Expected value by standing
Hit Return:Product of probability and hit expected value
Stand Return:Product of probability and stand expected value
The right two cells of the bottom row show that overall the expected value of hitting is -0.105807 and for standing is -0.102375. So, the table shows the odds favor standing by 0.00343.
To confirm these results I ran two simulations under the rules in question, one simulation hitting and one standing on this play. I counted only hands where soft 18 against a dealer ace happened at any time during play. Here are my results.
Soft 18 Vs Ace Simulation
| Soft 17 | Hands Played |
Total Win |
Expected Value |
| Stand | 3857490 | -396224 | -0.102715 |
| Hit | 3208390 | -337572 | -0.105215 |
So, the simulation shows the odds favor standing by 0.0025 over all possible scenarios where this hand turns up. Thus, for practical purposes of playing all hands, the best play is to stand, contrary to what my basic strategy chart says.
Mathias from Berlin, Germany
The Ultimate Casino Guide has various top ten lists. Here is their list of the ten most elegant casinos in alphabetical order.
- 50 St. James, London, England
- Atalantis at Paradise Island, Nassau, Bahamas
- Casino Baden-Baden, Germany
- Casino Bellevue Marienbad, Czech Republic
- Casino de Montreal, Montreal Quebec
- Le Casino, Monte Carlo
- St. James Club, Antigua
- Taleon Club, Saint Petersburg, Russia
- Venetian, Las Vegas, Nevada
Tifanny from Vancouver
Three hours at the gym sounds fishy to me too, not to mention working overtime the same amount of time. If he is cheating then nagging him with circumstantial evidence will not make him stop. It will just make him try harder to avoid detection. My advice is act like you believe him and hire a private investigator to tail him. You want him to have his guard down, he will be easier to catch that way. If it turns out you’re right get as far away from the bum as possible. Until then you don’t have enough evidence to be making any accusations.
Hector from Cardiff, UK
Thanks. I explain how I calculate the risk of ruin in video poker in my video poker appendix 1. However for games where the bet amount is not always the same the calculations get very messy and computer simulations are necessary.
"Anonymous" .
My Jacks or Better section shows the return of a 940/9/6 game to be 0.999030. The return from the royal is 0.024686. So the return from the other hands must be 0.999030-0.024686 = 0.97434. Although the probability of a royal is shown as 0.000026, that is only to two significant digits. Let’s use the return divided by the win, or 0.024686/940 as the probability. If j is the jackpot amount solve for j in the following equation:
1=0.97434 + j*(0.024686/940)
j = (1-0.97434)/(0.024686/940) = 977.33182.
So the breakeven point is a meter of 977.33 bet units or $4886.66. This assumes perfect 940/9/6 strategy. However few people know 940/9/6 strategy. If using 800/9/6 strategy then we would use the 800/9/6 table:
1 = (0.99543904-0.01980661) + j*(0.01980661/800)
j = (1 - (0.99543904-0.01980661))/(0.01980661/800)
j = 984.2197
So if using 800/9/6 strategy the jackpot would need to reach 984.22 bet units or $4921.10.
Ed from Indianapolis
As I’ve said before you need to gather some evidence. If you’re not sure how they are cheating then a simple tally of total initial bets made and units lost will suffice. You should flat bet one hand at a time, play perfect basic strategy, and do not count money bet doubling and splitting towards number of bets made. If based on your results the probability of your losses are less than 1 in 10,000 I think there is reason to be suspicious, and would be interested in seeing your evidence so that I may try to corroborate it. Based on a house edge of 0.5% and a standard deviation of 1.15 here is how much you need to be down according to the number of hands. This is based on total hands played since you started keeping track.
0.01% Losing Percentile in Blackjack
| Hands | Net Loss |
| 100 | 43 |
| 200 | 61 |
| 500 | 98 |
| 1000 | 140 |
| 2000 | 201 |
| 5000 | 327 |
| 10000 | 478 |
Carol from Reno
I asked Barney Vinson, author of Ask Barney: An Insider’s Guide to Las Vegas this question. He speculated it is a carry-over from the days of illegal gambling, but had no idea why the illegal tables used green felt. This is just a theory but I believe it is because pool table felt is usually green. The makers of gambling tables probably found green felt in the greatest supply because of the abundance of pool tables. However that begs the question, why do pool tables use green felt? I did some searching and found this explanation:
"The History of billiards is long and very rich. The game has been played by kings and commoners, presidents, mental patients, ladies, gentlemen, and hustlers alike. It evolved from a lawn game similar to the croquet played some-time during the 15th century in Northern Europe and probably in France. Play moved indoors to a wooden table with green cloth to simulate grass, and a simple border was placed around the edges." - Dolly’s Pro Shop
Andrew from New York City
You put each other on the spot with this question, which is almost always a big mistake. Maybe she just wanted to satisfy her curiosity or get a boost to her self-esteem from your confession. After the smoke cleared there was no mystery any longer. So I think she is lowering the temperature because she has no use for you any longer. My advice is let it go.
